Frantsuzova, Anastasia ORCID: https://orcid.org/0000-0001-9489-5295 (2021) Prior distributions for stochastic matrices. PhD thesis, University of Leeds.
Abstract
Right-stochastic matrices are used in the modelling of discrete-time Markov processes, with a property that the matrix elements are non-negative and each row sums to one. If we consider the problem of estimating these probabilities from a Bayesian standpoint, we are interested in constructing sensible probability distributions that can be used to encapsulate expert beliefs about such structures before any data is observed. Through the process of expert elicitation, this un- certainty can be represented in terms of probability distributions. In this thesis, we explore multivariate distributions on the simplex support from the view of expert elicitation. We explore properties and constraints of these distributions, and ways to elicit expert judgement about their parameters. This is interesting both mathematically and from a practical standpoint, particularly where there are many such variables to explore, which can prove cognitively challenging and tiring for the experts.
Similarly, data representing proportions of a whole can be unified into the com- positional framework (Aitchison, 1986) with similar non-negativity and unit-sum properties. This thesis also explores the study of compositional data analysis, its problems and modern ways of approaching them. Application of these methods is found in exploring how high resolution imagery obtained over rural areas could be used in order to identify the distribution of tree species found in those areas where monitoring is prohibited.
Metadata
Supervisors: | Aykroyd, Robert and Kent, John and Gosling, John Paul |
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Awarding institution: | University of Leeds |
Academic Units: | The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Identification Number/EthosID: | uk.bl.ethos.855575 |
Depositing User: | Ms Anastasia Frantsuzova |
Date Deposited: | 07 Jun 2022 15:24 |
Last Modified: | 11 Jul 2022 09:53 |
Open Archives Initiative ID (OAI ID): | oai:etheses.whiterose.ac.uk:30277 |
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